Can humans run upside-down loops?

Question

No skateboard, snowboard, etc..
running

Answer 1

Thats an interesting question. On paper, it seems like it would be possible, but I have a hard time imagining it working. Here are my calculations.

For a human to do a "loop the loop", he would need to run fast enough so that at the top of the loop, the centripital acceleration of his CENTER OF GRAVITY would be at least as great as gravitational acceleration.

Centripital acceleration = (speed)^2 / radius
Acceleration due to gravity (g) = 9.8 m.secs^2 downward

R is the radius of the loop, H is the persons height.
We will assume that the persons center of gravity is H/2 meters above the ground.

As the person runs through the loop, his center of gravity will travel a circle of radius R-H/2. If his running speed is V, the speed of his center of gravity will be V[1-H/(2R)].

(speed)^2 /radius > g
speed^2 > (9.8) radius
V^2[1-H/(2R)]^2 > (9.8)[R-H/2]
V^2[2R-H]^2 > (9.8)2R^2[2R-H]

v^2 > 2(9.8)R^2/[2R-H]

V > 19.6R/SQRT[2R-H]

Let us now assume that the person is 2 meters tall. The diameter of the circle must be at least that much. We will assume it is 4.0 meters, so the radius would be 2 meters.

speed > (19.6)(2.0)/SQRT(4-2) = 7 meters per second

A person 2 meters high who can manage to be running 7 meters per second at the top of a loop of diameter 4 meters should be able to do it....

Answer 2

heartsensei already has all the calculations, so I'm not going to bother adding more. I will however add in my two cents. If you consider that the world's fastes 100 m was done in a little under 10 seconds, you're basically running at 10 m/s. That kind of velocity is more than sufficient to overcome your force due to gravity. As long as you can continue to have a grip on the loop, you can run it.

Just don't try this at home.


And the person's height does not have anything to do with the actual problem. Unless it's a midget who can't run with stubby legs or something.

Answer 3

Maybe 7m/s is enough theoretically - maybe with roller skates, but I think once you start to think about how people run (with legs, not wheels, for instance) you see why it's harder. For instance, walking is only 60% efficient (on flat ground, and not running), which means humans need traction to maintain speed, and that will fall to zero at the top of the loop (minimum speed). Another thing is stride length. Someone 1.5m tall, with maybe 0.7m legs, should run with a stride of something like 1.1m. If your loop is 2m in diameter, 6.28m in circumference, that's only about 3 steps to the top, a 180 degree rotation, so about 60-degrees per step.

Another thing is humans are not rigid, we're a little spring-like, we compress and store kinetic energy as potential energy. There's some time constant there too and it could work out badly. This is all going to be tough to pull off... beware of approximating a person as a point in space, and thus...

Answer 4

The primary quandary with helicopters is they ought to be upright to get elevate, if you happen to spotted the helicopter will he approached the turn from a top altitude, then entered a steep dive. As the helicopter pulled up it is going to have highest elevate from the rotors, the pilot will then throw the helicopter the wrong way up into the loop. At the factor while the rotors are above 15degrees attitude of assault they produce no elevate, luckily the helicopter has sufficient pace to do the entire roll.

Answer 5

It depends on the diameter of the loop.

Answer 6

I don't think humans can run fast enough so that the centrifugal force of their running equals or exceeds their weight.